"2 Broke Girls" has appealing co-stars, a quite functional premise, considerable raunch, a favorable time-slot and one inherent problem: While CBS has enjoyed solid success with its Monday comedies, programs dominated by female leads generally haven't been among them.

Taking inventory of its assets and debits, “2 Broke Girls” has appealing co-stars, a quite functional premise, considerable raunch, a favorable time-slot and one inherent problem: While CBS has enjoyed solid success with its Monday comedies, programs dominated by female leads generally haven’t been among them. Whether “Girls” can reverse that trend remains to be seen, and will perhaps depend in part on how handsomely the new-look “Two and a Half Men” does in sustaining an audience — and propping up the entire night — beyond its inevitable initial rush of curiosity.

The Eye network has seemingly scored a coup by landing Kat Dennings as Max, a blunt, sexy, cash-strapped Manhattan waitress introduced putting a couple of grungy patrons in their place, telling one dude that snapping his fingers to demand service “dries up my vagina.”

In walks Caroline (Beth Behrs), the blond, leggy, Paris Hilton-like heiress to a fortune that has disappeared faster than you can say “Bernie Madoff.” (From a programming standpoint, given the plot of “Damages” last season and a similar wrinkle in ABC’s “G.C.B.,” the Madoff scandal has become the narrative gift that keeps on giving.)

Perky but impoverished, Caroline needs a job, which doesn’t exactly provoke cartwheels from Max. Still, she takes a degree of pity on her, after grilling her about what it’s like to be rich and have a pony.

That the two will end up living together, “Odd Couple” style, is never in doubt. Still, producersMichael Patrick King (“Sex and the City”) and Whitney Cummings (whose prospects looks considerably better here than in her new NBC sitcom) — aided by the sure hand of pilot maestro James Burrows — still manage to have fun getting there. “Oh my God, you were robbed!” Caroline shouts upon her first glimpse of Max’s sparsely furnished apartment.

Beyond the well-cast leads — with Dennings enjoying the meatier role but Behrs holding her own — the show distinguishes itself by being almost as dirty as “Men,” albeit from a female perspective, with a lot of lascivious sighing about the chiseled abs of a guy Max is dating. There’s also broad (if not especially strong) comic relief, including “Saturday Night Live” original Garrett Morris and Matthew Moy as the diner’s owner.

Not that naughtiness alone will be enough to secure “Girls’?” future where it counts, or by itself make the show feel like one of the boys. Still, if this promising half-hour finally comes up short on Nielsen’s balance sheet, it won’t be due to a deficit of energy or charm.